Monday 4 March 2024

On This Day in Math - March 4


This granite memorial, to William Willett, is in a clearing in Petts Wood in south east London. On the south face of the memorial is a sundial that is "set" to British Summer Time (BST) *

There is no philosophy which is not founded upon knowledge of the phenomena, but to get any profit from this knowledge it is absolutely necessary to be a mathematician.
~Daniel Bernoulli

The 63 day of the year; in Roman Numerals 63 is LXIII. If you represent each of these letters by its number in the English alphabet you get 12+24+9+9+9=63. (There is one more number that has this quality.)

At right, in honor of my many students from Misawa, Aomorishi, Japan, is Print 63 of Utagawa Hiroshige's 100 views of Edo (Koi No Bori)

\( \phi(63) = 36\)  The number of positive integers which are less than 63 and relatively prime to it.

63 can be expressed as powers of its digits, \( 6^2 + 3^3 = 63\)

63 is the Fourth Woodall Number.  Numbers of the form n*2<sup>n</sup>-1.  63 = 4*2,sup>4</sup> -1 Woodall Numbers were used in the study of testing prime numbers.  There is only one more Woodall Number that is a Day of the Year.

The Five Factorials Game, 2! * 5! / 3! + 4! - 1! = 63

63 is the smallest whole number that can be divided by any number from 1 to 9 without repeating decimals. (What's Next?)

And more Math Facts For Day 63 at Number Facts for Every Year Day (61-90) from On This Day in Math


1675 date of Charles II’s Royal Warrant that ordered the Board of Ordnance to pay for “the support and Maintenance” of John Flamsteed, appointed “our astronomical observator” and charged:

“to apply himself with the most exact care and diligence to the rectifying the tables of the motions of the heavens, and the places of the fixed stars, so as to find our the so much-desired longitude of places for the perfecting the art of navigation.”

*Rebekah Higgitt, Teleskopos (although Ms. Higgitt is not fond of historical anniversaries)

The Royal Observatory web page contains a little more information about the events that precipitated the founding of the observatory:

If you'd stood here on the hill in Greenwich Park on 10 August 1675 you would have seen an important event. At 3.14pm the first Astronomer Royal John Flamsteed laid the foundation stone of the new Royal Observatory, Britain’s first state-funded scientific research institution. Events had moved quickly after the initial visit by the French astronomer, Sieur de St. Pierre in December 1674. Thanks to Charles II’s French mistress, Louise de Kéroualle, rumours started to circulate at court that St. Pierre had devised a means of determining longitude at sea by using observations of the Moon’s position in relation to the background stars. Improving navigation at sea was a major challenge for 17th century merchants and their sailors who undertook long voyages across the globe to bring back precious cargoes of tea, spices, timber, porcelain and textiles. While the French astronomer’s claims were rejected by a committee of English scholars in February 1675, the emergence of this idea highlighted the need for something to be done to address this challenge which offered many lucrative financial and political benefits. On 4 March 1675, the King signed a Royal Warrant appointing Flamsteed as 'astronomical observator..[..] as to find out the so much-desired longitude of places for the perfecting the art of navigation'.


1801 Thomas Jefferson became the third president of the United States. During his two terms in office he repeatedly sponsored bills providing governmental support of science for the common good. *VFR

1837 Adolphe Quetelet Predicts a meteor shower for the night of August 10th. First published prediction that Persid meteors were annual event.
The 1833 Leonid storm had galvanized interest in meteors, and the time was ripe. Adolphe Quetelet, a Belgian statistician and founder and director of the Brussels Observatory, had mentioned mid-August meteors very tentatively six months earlier. His attention had been called to meteors by François Arago of France, who dominated European science at the time with his skill in discerning important scientific problems and suggesting experiments to solve them. What, asked Arago in the wake of the 1833 display, constituted a shower of meteors, and what was the rate of the ordinary, everynight drizzle?
The problem was ideal for Quetelet, whose passion was statistics. In a speech to the Royal Academy of Sciences and Arts of Brussels on December 3, 1836, Quetelet gave his answer: averaged over the night and year, a single observer should expect to see eight sporadic (nonshower) meteors per hour. That figure is still good today. After his speech Quetelet made a brief mention of unusual August meteors, and in his 1836 annual report of the Brussels Observatory he presented the idea timidly and almost in passing: "I thought I also noticed a greater frequency of these meteors in the month of August (from the 8th to the 15th)."
By the following year, Quetelet had accidentally found records in his observatory of exceptional meteor displays on August 10th of 1834 and 1835 to accompany the increase he had seen in 1836. He called for scientists at the March 4, 1837, session of the Royal Academy of Brussels to watch the sky on August 10, 1837. *Sky and Telescope


1891 David Hilbert submits article on his space filling curve, Über die stetige Abbildung einer Linie auf ein Flächenstück to the journal Mathematische Annalen. *Wik

 Applications of the Hilbert curve are in image processing: especially image compression and dithering.

1929 When Herbert Hoover was sworn in as President of the United States, his wife, Lou Henry Hoover, became the first “First Lady” with a degree in a scientific field. Like her husband, she had graduated from Stanford with a degree in geology. *FFF pg 313
Ben Gross added, "I'm pretty sure that Lou Henry Hoover is the only First Lady to be featured as @LindaHall_org's #ScientistOfTheDay!" I would not doubt him. 

She spoke five languages by the time she became first lady.

On March 9, 1914, the Mining and Metallurgical Society of America held a dinner to be-stow the Society’s first gold medal on Herbert Hoover (1874 – 1964) and his wife Lou Henry Hoover (1874-1944) to honor their joint translation and annotation of a treatise on mining,

 De Re Metallica.

 Written by the German polymath Georgius Agricola (1494-1555) , the original work was published in 1556 in medieval Latin and had never before been adequately translated and decoded into a comprehensible modern language. Agricola was revered by such intellectual giants as the explorer Alexander von Humboldt and the poet Goethe, both of whom had worked as mining managers as young men. The treatise was often consulted,but rarely completely understood until the Hoovers’ English version was first published in 1912-1913. (It was the first English translation. *PB) The footnotes contain lengthy essays on the history of metallurgy and its role in civilization. The Hoovers’ thesis is expressed at the end of their introduction: “Science is the base upon which is reared the civilization of today.” In accordance with protocol, Herbert Hoover’s name came rst on the title page, then his wife’s name. Both Hoovers held bachelors degrees in geology from Stanford. While he wasa brilliant manager, Herbert Hoover was better at mathematics than languages and almost did not graduate from Stanford because of his deficient English. He failed his German class and never learned Latin. The members of the engineering profession in the United States knew the high-profile couple well, and understood what his remarkable pragmatic talents were,and also what her extraordinary intellectual talents were. The March 14, 1914 edition of the Engineering & Mining Journal simply stated what everyone knew:“In all of Mr. Hoover’s literary work,Mrs.Hoover has been an important collaborator. In the preparation of his ‘Principles of Mining’ she revised the manuscript, read the proofs and saw the work through the press, remaining in New York for that purpose after Mr. Hoover had been called away. In the translation of Agricola, her collaboration was more important. She accompanied Mr. Hoover in his travels of investigation, joined in his studies of the history of mining, and bore the brunt of the translation of corrupt, medieval Latin into fluent and accurateEnglish.” 

An interesting anecdote I heard, which perhaps,someone can verify or refute, is that after his aid work to support the restoration of Europe after WWI, in one of the countries "to Hoover" means to help.

1949 The first time the carbon-14 radioactive dating technique was used. To test the theory the method was used to determine the age of Egyptian artifacts where their age was already known. Willard Frank Libby dated a piece of wood from the Third Dynasty Pharaoh Djoser's tomb that was about 4,700 years old. This age was nearly the same as the half-life of carbon-14, they expected the concentration of carbon-14 would be half that found today. This test was successful. *

In 1960, he was awarded the Nobel Prize in Chemistry "for his method to use carbon-14 for age determination in archaeology, geology, geophysics, and other branches of science". He also discovered that tritium similarly could be used for dating water, and therefore wine.

1956 An Wang Sells Core Memory Patent to IBM:
An Wang sells his patent for ferrite core memory to IBM for \($500,000\). One of the most important inventions in computer history, ferrite core memory was widely used in digital computers from the mid-1950s until the mid-1970s. The U.S. Patent Office awarded Wang the patent for what he called a pulse transfer controlling device in 1949. Jay Forrester at MIT is considered the inventor of core memory. *CHM

In 1977, the first Freon-cooled Cray-1 supercomputer, costing \($19,000,000\) , was shipped to Los Alamos Laboratories, NM, and was used to help the defense industry create sophisticated weapons systems. This system had a peak performance of 133 megaflops and used the newest technology, integrated circuits and vector register technology. The Cray-1 looked like no other computer before or since. It was a cylindrical machine 7 feet tall and 9 feet in diameter, weighed 30 tons and required its own electrical substation to provide it with power (an electric bill around \($35,000/month\)). The inventor, Seymour Cray, died 5 Oct 1996 in an auto accident. His innovations included vector register technology, cooling technologies, and magnetic amplifiers. *TIS

1979 Voyager I photo reveals rings of Jupiter. *VFR  The first evidence of a ring around the planet Jupiter is seen in this photograph taken by Voyager 1 on March 4, 1979. The multiple exposure of the extremely thin faint ring appears as a broad light band crossing the center of the picture.


The 2007 Parliamentary elections held on Estonia on this day were the world’s first nationwide election where voting was allowed over the Internet. A little over 30,000 out of 940,000 registered Estonian voters participated in Internet voting that year, which was conducted from February 26-28 prior to the election. Voters had to use their state-issued ID and enter two passwords to cast their votes online. From the 3.4% of voters who voted over the Internet in 2007, nearly 44% of Estonian voters did so in their 2019 elections.


in 2012 Today's date could be written (yr/mo/day) as 12/3/4 (I missed this until it was pointed out to me by Don McDonald)

in 2023, next month on April 5 would be 23/4/5.  


1822 Jules Antoine Lissajous (4 March 1822 in Versailles, France - 24 June 1880 in Plombières, France) was a French mathematician best known for the Lissajous figures produced from a pair of sine waves. *SAU The curves are also called (and perhaps should always be called) Bowditch curves for the early American mathematician, Nathanial Bowditch,  who worked with them earlier. In general, a parametric curve with equations x= A sin(k t ); y= B sin(m t), the curves can describe things as simple as a circle or ellipse to more complex open and closed curves. If the ratio of k/m is rational, the curve will eventually close.(EEB)

Lissajous was interested in waves and developed an optical method for studying vibrations. He wanted to be able to see the waves that were created by vibrations, usually expressed in the form of sound. At first he studied waves produced by a tuning fork in contact with water, studying the ripples that were caused. Working on these ideas, he published Sur la position des noeuds dans les lames qui vibrent transversalement (1850). In 1855 he described a way of studying acoustic vibrations by reflecting a light beam from a mirror attached to a vibrating object onto a screen. *SAU

1833 John Monroe Van Vleck (March 4, 1833–November 4, 1912) was an American mathematician and astronomer. He taught astronomy and mathematics at Wesleyan University in Middletown, Connecticut for more than 50 years (1853-1912), and served as acting university president twice. The Van Vleck Observatory (at Wesleyan University) and the crater Van Vleck on the Moon are named after him. *Wik

1854 Sir (William) Napier Shaw (4 Mar 1854; 23 Mar 1945 at age 90) was an English meteorologist who applied his training in mathematics. He studied the upper atmosphere, using instruments carried by kites and high-altitude balloons. He measured (1906) the movement of air in two anti-cyclones, finding descent rates of 350 and 450 metres per day. He calculated the reduction in pressure due to a certain depression to correspond to the removal of two million million tons of air. He introduced the millibar unit for measurement of air pressure (1000 millibar = 1 bar = 1 standard atmosphere) and the tephigram to illustrate the temperature of a vertical profile of the atmosphere. He also co-authored an early work on atmospheric pollution, The Smoke Problem of Great Cities (1925).*TIS

Annotated tephigram *Wik

1862 Robert Emden (4 Mar 1862, 8 Oct 1940) Swiss astrophysicist and mathematician who wrote Gaskugeln (Gas Spheres, 1907), giving a mathematical model of stellar structure as the expansion and compression of gas spheres, wherein the forces of gravity and gas pressure are in equilibrium. He expanded on earlier work by J. H. Lane (1869) and A. Ritter (1878-83) who first derived equations describing stars as gaseous chemical, spherical bodies held together by their own gravity and obeying the known gas laws of thermodynamics. For four decades, the Lane-Emden equation was the foundation of theoretical work on the structure of stars: their central temperatures and pressures, masses, and equilibria. Emden also devised a hypothesis, no longer taken seriously, to explain sunspots. *TIS

Lane Emden Equation, *Wik

1866 Eugène Maurice Pierre Cosserat (4 March 1866 in Amiens, France - 31 May 1931 in Toulouse, France) Cosserat studied the deformation of surfaces which led him to a theory of elasticity. *SAU

1881 Richard C(hace) Tolman (4 Mar 1881, 5 Sep 1948) was an American physicist and chemist who demonstrated that electrons are the charge-carrying entities in the flow of electricity, and also made a measurement of its mass. During the Manhattan Project of WW II, he was the chief scientific adviser to Brig. General Leslie Groves, the head of military affairs overseeing the development of the atomic bomb. After the war he was adviser to the U.S. representative to the United Nations Atomic Energy Commission. *TIS

Each year, the southern California section of the American Chemical Society honors Tolman by awarding its Tolman Medal "in recognition of outstanding contributions to chemistry."

1889 Oscar Chisini (March 4, 1889 – April 10, 1967) was an Italian mathematician. He introduced the Chisini mean (The arithmetic, harmonic, geometric, generalised, Heronian and quadratic means are all Chisini means, as are their weighted variants) in 1929. In 1929 he founded the Institute of Mathematics (Istituto di Matematica) at the University of Milan, along with Gian Antonio Maggi and Giulio Vivanti. He then held the position of chairman of the Institute from the early 1930s until 1959.The Chisini conjecture in algebraic geometry is a uniqueness question for morphisms of generic smooth projective surfaces, branched on a cuspidal curve. A special case is the question of the uniqueness of the covering of the projective plane, branched over a generic curve of degree at least five. *Wik

1904 George Gamow (4 Mar 1904,19 Aug 1968) Russian-born American nuclear physicist, cosmologist and writer who was one of the foremost advocates and developer of Lemaître's Big Bang theory, which describes the origin of the universe as a colossal explosion that took place billions of years ago. In 1954, he expanded his interests into biochemistry and his work on deoxyribonucleic acid (DNA) made a basic contribution to modern genetic theory. *TIS

Gamow discovered a theoretical explanation of alpha decay by quantum tunneling, invented the liquid drop model and the first mathematical model of the atomic nucleus, worked on radioactive decay, star formation, stellar nucleosynthesis, Big Bang nucleosynthesis (which he collectively called nucleocosmogenesis), and molecular genetics.

At the  University of Leningrad, Gamow made friends with three other students of theoretical physics, Lev Landau, Dmitri Ivanenko, and Matvey Bronshtein. The four formed a group they called the Three Musketeers, which met to discuss and analyze the ground-breaking papers on quantum mechanics published during those years. He later used the same phrase to describe the Alpher, Herman, and Gamow group.

In his middle and late career, Gamow directed much of his attention to teaching and wrote popular books on science, including One Two Three... Infinity and the Mr Tompkins series of books (1939–1967). Some of his books remain in print more than a half-century after their original publication.


1914 Robert Rathbun Wilson (4 Mar 1914, 16 Jan 2000) was an American physicist who was the first director of Fermilab. From 1967, he led the design and construction of Fermilab (the Fermi National Accelerator Laboratory) near Chicago, Illinois. He also improved the environment by restoring prairie at the site. It began operating in 1972 with the world's most powerful particle accelerator. With later improvements, it retained that status for well over three decades until it was superceded by the LHC (Large Hadron Collider) at the CERN laboratory in Geneva, Switzerland. Wilson is remembered for his justification of the needed financing at a Senate hearing in 1969, where he said “It has nothing to do with defending our country, except to make it worth defending.” He resigned in 1978 because he did not believe the government was giving it sufficient funding for its research mission.*TIS The stately 16-story Robert Rathbun Wilson Hall rises above the surrounding Illinois countryside. Inspired by a Gothic cathedral in Beauvais, France, its twin towers are joined by crossovers beginning at the seventh floor. Spent a wonderful week there one summer in pursuit of knowledge in non-linear dynamics.

1923 Patrick (Alfred Caldwell) Moore, (4 Mar 1923, )English amateur astronomer, writer and broadcaster. He was educated at home due to childhood illness, from which time he acquired his interest in observational astronomy. Moore is best known as the enthusiastic and knowledgeable presenter of the BBC TV program The Sky at Night, which he began in 1957. With a half-century of broadcasts, this is the world's longest-running television series, and it remains so with the original presenter. Moore has written over 60 books, including The Amateur Astronomer (1970), The A-Z of Astronomy (1986), and Mission to the Planets (1990). As an accomplished xylophone player, his interest in astronomy also shows in the title of one of his musical compositions: Perseus and Andromeda (1975)*TIS


1816 Josef (also José or Joseph) de Mendoza y Ríos (29 January 1761; Sevilla, Spain - 4 March 1816 Brighton, England) was a Spanish astronomer and mathematician of the 18th century, famous for his work on navigation. The first work of Mendoza y Ríos was published in 1787: his treatise, Tratado de Navegación, about the science and technique of navigation in two tomes. He also published several tables for facilitating the calculations of nautical astronomy and useful in navigation to calculate the latitude of a ship at sea from two altitudes of the sun, and the longitude from the distances of the moon from a celestial body.
In the field of the nautical instruments, he improved the reflecting circle.
In 1816, he was elected a foreign member of the Royal Swedish Academy of Sciences. @Wik

1910 Knut Johan Angstrom (12 Jan 1857; 4 Mar 1910) Swedish physicist, son of Anders Angstrom, who invented an electric compensation pyrheliometer and other devices for infra-red photography. With these, he studied the sun's heat radiation*TIS

1915 William Willett (10 Aug 1856, 4 Mar 1915 at age 58)English builder who invented Daylight Saving Time. He claimed he had the idea while taking an early summer morning ride in Petts Wood near to his home in Chislehurst, London. He observed that many blinds were still down, although there was already good daylight, yet many made no use of it. He used his wealth as a prominent home builder to campaign for a scheme of adjusting clocks with the season and published a pamphlet in 1907. His original idea was to make four weekly changes of 20-mins each, for a total of 80-mins. The first Daylight Saving Bill, proposing a single one hour at the change of season failed in 1908. After his death, the idea was adopted during WW I for wartime fuel savings. A memorial was erected in Petts Wood.*TIS A sun dial Memorial was erected in the Petts Wood in his honor.*TIS

1976 Walter Schottky (23 Jul 1886, 4 Mar 1976 at age 89)Swiss-born German physicist whose research in solid-state physics led to development of a number of electronic devices. He discovered the Schottky effect, an irregularity in the emission of thermions in a vacuum tube and invented the screen-grid tetrode tube (1915). The Schottky diode is a high speed diode with very little junction capacitance (also known as a "hot-carrier diode" or a "surface-barrier diode.") It uses a metal-semiconductor junction as a Schottky barrier, rather than the semiconductor-semiconductor junction of a conventional diode. *TIS

1997 Robert Henry Dicke (6 May 1916 St. Louis, Missouri, USA - 4 Mar 1997 at age 80) American physicist who worked in such wide-ranging fields as microwave physics, cosmology, and relativity. As an inspired theorist and a successful experimentalist, his unifying theme was the application of powerful and scrupulously controlled experimental methods to issues that really matter. He also made a number of significant contributions to radar technology and to the field of atomic physics. His visualization of an oscillating universe stimulated the discovery of the cosmic microwave background, the most direct evidence that our universe really did expand from a dense state. A key instrument in measurements of this fossil of the Big Bang is the microwave radiometer he invented. His patents ranged from clothes dryers to lasers. *TIS


2000 Hermann Alexander Brück (15 August 1905 in Berlin, Germany – 4 March 2000 in Edinburgh, Scotland) was a German-born astronomer who spent the great portion of his career in the United Kingdom.
Upon graduation from Munich, Brück followed his friend Albrecht Unsöld to the Potsdam Astrophysical Observatory; Unsöld had earned his doctorate the year before, also under Sommerfeld. While there, he participated in the physics colloquium at the Humboldt University of Berlin with the physicists Max von Laue and Albert Einstein and the astronomer Walter Grotrian. With growing difficulties under National Socialism, Brück left Germany in 1936 to take a temporary research assistantship at the Vatican Observatory. In 1937 he moved to the University of Cambridge to join the circle of the modern astrophysicists around Arthur Eddington. In time, Brück became Assistant Director of the Observatories and John Couch Adams, specializing in solar spectroscopy. He taught a course in classical astronomy and started the student astronomical society, which fostered the careers of many astronomers.
In 1947, at the invitation of Éamon de Valera, Brück moved to Dublin to direct the Dunsink Observatory, which was part of the Dublin Institute for Advanced Studies, where he associated with Erwin Schrödinger. In 1950, the Observatory, along with the Royal Irish Academy, hosted the first meeting of the Royal Astronomical Society. In 1955, the International Astronomical Union held their triennial Assembly in Dublin. At this gathering, the Observatory demonstrated photoelectric equipment for photometry, which had been developed by M. J. Smyth, who had been Brück’s student in Cambridge. Also displayed was the UV solar spectroscopy which extended the Utrecht Atlas and formed part of the revised Rowland tables of the Solar spectrum; Brück’s wife, Dr. Mary Brück (née Conway), was a leading figure in this work.
In 1957, Brück moved to the University of Edinburgh. With his vision and drive, he transformed the Royal Observatory into an internationally-ranked center of research. He put together a team of astronomers and engineers headed initially by P. B. Fellgett and later by V. C. Reddish *Wik

2011 Simon van der Meer (24 Nov 1925, 4 March, 2011)Dutch engineer and physicist who along with Italian physicist Carlo Rubbia, discovered the W particle and the Z particle by colliding protons and antiprotons, for which both men shared the Nobel Prize for Physics. These subatomic particles (units of matter smaller than an atom) transmit the weak nuclear force, one of four fundamental forces in nature. The discovery supported the unified electroweak theory put forward in the 1970's. Working at CERN in Switzerland, Van der Meer improved the design of particle accelerators used produce collisions between beams of subatomic particles. He invented a device that would monitor and adjust the particle beam with correcting magnetic fields by a system of 'kickers' placed around the accelerator ring.*TIS

Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell

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